1. Mathematical challenges for able pupils
Year 1 B Securing number facts, understanding shape

2. Choose from these numbers.
Pick a pair
Choose from these numbers. 1 3 5 7
1. Pick a pair of numbers.
Add them together.
Write the numbers and the answer.
Pick a different pair of numbers.
Keep doing it. How many different answers can you get?
2. Now take one number from the other.
How many different answers can you get now?
Learning Objective:
Solve mathematical problems or puzzles.
Know addition and subtraction facts up to 10.

3. Solution to the Pick a pair problem.
There are six different sums and
six different (positive) differences.
= – 1 = 2
1 + 5 = – 3 = 2
2 + 7 = – 1 = 4
3 + 5 = – 5 = 2
3 + 7 = – 3 = 4
5 + 7 = – 1 = 6
Adapt the puzzle by using larger numbers.
Learning Objective:
Solve mathematical problems or puzzles.
Know addition and subtraction facts up to 10.

4. 1 2 3 4 5 6 7 8 9 Card sharp Take ten cards numbered 0 to 9.1 2 3 4 5 6 7 8 9
1. Pick three cards with a total of 12. You can do it in 10 different ways.See if you can record them all.
On your next click you will find the answers.
2. Now pick four cards with a total of 12. How many different ways can you do it?
3. Can you pick five cards with a total of 12?
Learning Objective:
Solve mathematical problems or puzzles.
Know addition facts to at least 10.
Solve a problem by sorting, classifying and organising information

5. Solution to the problem.
1. There are 10 different ways to choose
three cards with a total of 12:
0, 3, 9 1, 2, 9 2, 3, 7 3, 4, 5
0, 4, 8 1, 3, 8 2, 4, 6 0, 5, 7
1, 4, 7 1, 5, 6
2. There are 9 different ways to choose
four cards with a total of 12:
0, 1, 2, 9 0, 2, 3, 7 1, 2, 3, 6 0, 1, 3, 8
0, 2, 4, 6 1, 2, 4, 5 0, 1, 4, 7 0, 3, 4, 5
0, 1, 5, 6
3. No.
Learning Objective:
Solve mathematical problems or puzzles.
Know addition facts to at least 10.
Solve a problem by sorting, classifying and organising information

6. Each duck went in a puddle. More than one duck can go in a puddle.
Ducks and puddles
Dan threw 3 rubber ducks.
Each duck went in a puddle.
More than one duck can go in a puddle.
The scores are written in the puddles.
2. Find three ways to score 6.
1. What is the highest score Dan can get?
3. Find three ways to score 9.
4. What other scores can Dan get?
Next click brings you the solutions...
Learning Objective:
Solve mathematical problems or puzzles.
Know addition facts up to 10.

7. Solution to the Ducks and Puddles problem.
1. The highest score is 12
(3 ducks in 4).
2. Score 6 in three ways:
1 duck in 4 and 2 ducks in 1, or 1 duck in 1, 1 duck in 2 and 1 duck in 3, or 3 ducks in 2.
3. Score 9 in three ways:
1 duck in 1 and 2 ducks in 4, or 1 duck in 2, 1 duck in 3, 1 duck in 4, or 3 ducks in 3.
4. Besides 6, 9 and 12, other possible
scores are:
3: 3 ducks in 1
4: 2 ducks in 1, 1 ducks in 2
5: 2 ducks in 1, 1 duck in 3, or
1 duck in 1, 2 ducks in 2
7: 1 duck in 1, 2 ducks in 3, or
2 ducks in 2, 1 duck in 3, or
1 duck in 1, 1 duck in 2, 1 duck in 4
8: 2 ducks in 2, 1 duck in 4, or
1 duck in 2, 2 ducks in 3, or
1 duck in 1, 1 duck in 3, 1 duck in 4
10: 1 duck in 2, 2 ducks in 4
Learning Objective:
Solve mathematical problems or puzzles.
Know addition facts up to 10.

8. Emma had some fireworks.
Some made 3 stars. Some made 4 stars.
Altogether Emma’s fireworks made 19 stars.
How many of them made 3 stars?
Find two different answers.
What if Emma’s fireworks made 25 stars?
Find two different answers.
Learning Objective:
Solve mathematical problems or puzzles.
Count on in steps of 3 or 4 from zero, or from any small number.

9. Solution for Fireworks
For 25 stars:
3 fireworks made 3 stars and 4 fireworks made 4 stars, or
7 fireworks made 3 stars and 1 firework made 4 stars
For 19 stars:
5 fireworks made 3 stars and 1 made 4 stars or
1 firework made 3 stars and 4 made 4 stars
Learning Objective:
Solve mathematical problems or puzzles.
Count on in steps of 3 or 4 from zero, or from any small number.

10. Thank You

11. References and additional resources.
These units were organised using advice given at:
PowerPoint template published by
These Mental Maths challenges can be found as a PDF file at :
The questions from this PowerPoint came from:
Mathematical challenges for able pupils in Key Stages 1 and 2
Corporate writer was Department for Education and Employment and it is produced under a © Crown copyright 2000
Contains public sector information licensed under the Open Government Licence v3.0. (
All images used in this PowerPoint was found at the free Public Domain Clip Art site. (